Question

HELP PLEASE

Use the value of the discriminant to determine the number and type of roots for the equation,
X^2 = 4x - 4
A. 2 real, irrational roots
B. 1 real, rational root
C. 2 complex roots
D. 2 real, rational roots

Answer 1

We are given –

`\qquad`
`\twoheadrightarrow\bf x² = 4x -4`

`\qquad`
`\twoheadrightarrow\bf x² -4x +4 = 0`

• Where, a = 1 ; b = -4 ; c = 4

Let's find it's discriminant.

We know –

`\qquad`
`\purple{\twoheadrightarrow\bf Discriminant = b² - 4ac}`

`\qquad`
`\twoheadrightarrow\sf Discriminant = (-4)² - 4 * 1 * 4`

`\qquad`
`\twoheadrightarrow\sf Discriminant = 16-16`

`\qquad`
`\purple{\twoheadrightarrow\sf Discriminant =0 }`

• If Δ (Discriminant) >0here are two separate real roots.
• If Δ (Discriminant) =0, there are two identical real roots.
• If Δ (Discriminant) <0, there are no real roots, but there are two complex roots.

As we got –

• Δ Discriminant is 0 that means , there are two identical real roots. Henceforth, Option (D) 2 real, rational roots – is correct.